lmomrevgum {lmomco} | R Documentation

## L-moments of the Reverse Gumbel Distribution

### Description

This function estimates the L-moments of the Reverse Gumbel distribution given the parameters (xi and α) from `parrevgum`. The type-B L-moments in terms of the parameters are

λ^B_1 = xi - (0.5722...) α - αlbracemathrm{Ei}(-log(1-zeta))rbracembox{,}

λ^B_2 = αlbracelog(2) + mathrm{Ei}(-2log(1-zeta)) - mathrm{Ei}(-log(1-zeta))rbracembox{,}

tau_3 = mbox{,}

tau_4 = mbox{, and}

tau_5 = mbox{.}

noindent where zeta is the right-tail censoring fraction of the sample o the nonexceedance probability of the right-tail censoring threshold, and mathrm{Ei}(x) is the exponential integral defined as

mathrm{Ei}(X) = int_X^{infty} x^{-1}e^{-x}mathrm{d}x mbox{,}

noindent where mathrm{Ei}(-log(1-zeta)) rightarrow 0 as zeta rightarrow 1 and mathrm{Ei}(-log(1-zeta)) can not be evaluated as zeta rightarrow 0.

### Usage

    lmomrevgum(para)

### Arguments

`para` | The parameters of the distribution.

### Value

An R `list` is returned.

`L1` | Arithmetic mean.
`L2` | L-scale—analogous to standard deviation.
`LCV` | coefficient of L-variation—analogous to coe. of variation.
`TAU3` | The third L-moment ratio or L-skew–analogous to skew.
`TAU4` | The fourth L-moment ratio or L-kurtosis—analogous to kurtosis.
`TAU5` | The fifth L-moment ratio.
`L3` | The third L-moment.
`L4` | The fourth L-moment.
`L5` | The fifth L-moment.
`zeta` | Number of samples observed (noncensored) divided by the total number of samples.
`source` | An attribute identifying the computational source of the L-moments: “lmomrevgum”.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1995, The use of L-moments in the analysis of censored data, in Recent Advances in Life-Testing and Reliability, edited by N. Balakrishnan, chapter 29, CRC Press, Boca Raton, Fla., pp. 546–560.

### See Also

`parrevgum`, `quarevgum`, `cdfrevgum`

### Examples

[Package lmomco version 0.92 Index]